Geometry Medians, centroids, triangle inequality

Front

What are the segments drawn from the vertices to the midpoints of the opposite sides in a triangle called?

Back

Medians

Front

If Z is the centroid of triangle XYZ, and ZX = 3, what is the length of AZ?

Back

9

Front

Can the segments of lengths 8, 15, and 24 form a triangle?

Back

No

Front

If G is the centroid of triangle ABC and AC = 32, what is the length of CE?

Back

16

Front

What is the range of values for the third side of a triangle if two sides measure 8 and 15?

Back

Between 7 and 23

Front

What is the definition of a centroid in a triangle?

Back

The centroid is the point where the three medians intersect, and it divides each median into a ratio of 2:1.

Front

What is the Triangle Inequality Theorem?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has sides of lengths 5, 12, and x, what is the range of possible values for x?

Back

Between 7 and 17.

Front

What is the relationship between the lengths of the medians and the sides of a triangle?

Back

The length of a median is always less than the length of the longest side of the triangle.

Front

How do you find the length of a median in a triangle?

Back

Use the formula: m = 1/2 * √(2a² + 2b² - c²), where a and b are the lengths of the sides adjacent to the median, and c is the length of the side opposite the median.